Improved Response Surface Method for Time-Variant Reliability Analysis of Nonlinear Random Structures Under Non-Stationary Excitations

The problem of time-variant reliability analysis of randomly driven linear/nonlinear vibrating structures is studied. The excitations are considered to be non-stationary Gaussian processes. The structure properties are modeled as non-Gaussian random variables. The structural responses are therefore non-Gaussian processes, the distributions of which are not generally available in an explicit form. The limit state is formulated in terms of the extreme value distribution of the response random process. Developing these extreme value distributions analytically is not easy, which makes failure probability estimations difficult. An alternative procedure, based on a newly developed improved response surface method, is used for computing exceedance probabilities. This involves fitting a global response surface which approximates the limit surface in regions which make significant contributions to the failure probability. Subsequent Monte Carlo simulations on the fitted response surface yield estimates of failure probabilities. The method is integrated with professional finite element software which permits reliability analysis of large structures with complexities that include material and geometric nonlinear behavior. Three numerical examples are presented to demonstrate the method.